Based on WRFV3 model, the Aircraft Meteorological Data Relay(AMDAR) data and NCEP reanalysis data were used to numerically simulate the 110 moderate or greater Clear Air Turbulence(CAT)observations and 196 no turbulence observations on transoceanic airlines over the surrounding waters of South China Sea in 2007. The applicability of turbulence indices (Brown Index, Horizontal Wind Shear Index, MOSCAT Index, Dutton Index, Turbulence Index I, Turbulence Index II) and their corresponding threshold were researched through calculating the probability of detection of "yes" observations, probability of detection of "no" observations, true skill statistic and equitable threat score of the preselected six turbulence indices. Results show that: (1) Brown index is the best diagnostic index of CAT on transoceanic airlines over the surrounding waters of South China Sea, especially when its threshold amounts to 3.2×10^-5. (2) The diagnosis of CAT on transoceanic airlines over the surrounding waters of South China Sea is significantly sensitive to the selection of threshold value.